### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Brian Nakamura**, Rutgers University, bnaka {at} math [dot] rutgers [dot] edu
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: On generating series of finitely presented operads and pattern avoidance

Speaker: ** Anton Khoroshkin**, Stony Brook University

Date: Thursday, December 13, 2012 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

An algebra of some type is a set with some operations on it. Let us remove the underlying set, what remains is the collection of all operations one can define. This collection with the prescribed rules of compositions is what one calls an operad.

In this talk I will explain the notion of operads and the theory of monomials for operads. The combinatorics of monomials in operads is governed by avoidance problems. In particular, the Hilbert series of dimensions of certain class of operads coincides with the generating series of permutations avoiding a given set of patterns. I will state several general results and conjectures about the class of generating series for monomial operads providing some computational algorithms for these series.

See: http://www.math.rutgers.edu/~bnaka/expmath/